Question

Write the sequence with $n$th term. Show that all the sequences form A.P $a_n=3+4n$

Answer 1

Given, the nth term of the sequence is

$a_n=4n+3...................eq\left(1\right)$

1) for finding the first term of sequence $\left(a_1\right)$ put n=1 in eq(1)

$a_1=4\times 1+3$

$⟹a_1=4+3$

$⟹a_1=7$

2) for finding the second term of sequence $\left(a_2\right)$put n=2 in eq(1)

$a_2=4\times 2+3$

$⟹a_2=8+3$

$⟹a_2=11$

3) for finding the third term of sequence $\left(a_3\right)$ put n=3 in eq(1)

$a_3=4\times 3+3$

$⟹a_3=12+3$

$⟹a_3=15$

4) for finding the fourth term of sequence $\left(a_4\right)$ put n=4 in eq(1)

$a_4=4\times 4+3$

$⟹a_4=16+3$

$⟹a_4=19$

5) for finding the fifth term of sequence $\left(a_5\right)$ put n=5 in eq(1)

$a_5=4\times 5+3$

$⟹a_5=20+3$

$⟹a_5=23$

and so on

hence this is an A.P and the sequence is given by

$7,11,15,19,23,.....$